Simulative Implementations of Fast Single-Qubit Quantum Logic Operations With Waveguides Based on Invariant Engineering

Quantum logic operations are the elemental operations for quantum computing and have been implemented in various time-evolved atomic systems. Here, we present a scheme to simulatively implement the typical quantum NOT- and Hadamard gates operations, alternatively with the coupled three-waveguide structure (rather than the usual atomic levels); two modes in sinuous waveguides encoding the two logic states of a qubit and the mode in the center straight waveguide serve as auxiliary the coupler. Based on the Lewis-Riesenfeld invariant theory, we show that the desired mode conversions for implementing the NOT gate and mode split to realize the Hadamard gate are fast achieved by engineering the coupling parameters between the optical waveguides. The implementations of the logic gates demonstrated here relay on the structure parameters of the waveguides, rather than the durations of time evolutions with the usual driven atomic systems, and thus should be feasible robustly with the current integrated optical technology.